Observer Based Sliding Mode Control: Equivalence with Classical Frequency Domain Control

In this article, we find an "on the average" equivalence between observer-based Sliding Mode control and classical output feedback compensation networks. The average output feedback control actions are found to be naturally implemented via a one-dimensional Delta-Sigma modulator circuit absorbing the underlying sliding regime defined in the state space. We focus on perturbed pure-integration switched systems, representing a paradigm of the input-output representation of an on-off controlled flat system. The simplified model is assumed to undergo endogenous (state-dependent) and exogenous disturbances in the form of a, lumped, total disturbance input. Experimental results are presented for the output trajectory tracking task on a single link manipulator-DC motor combination.

[1]  Igor Boiko,et al.  Frequency-Domain Methods in Conventional and Higher-Order Sliding Mode Control , 2011 .

[2]  Zhiqiang Gao,et al.  On stability analysis of active disturbance rejection control for nonlinear time-varying plants with unknown dynamics , 2007, 2007 46th IEEE Conference on Decision and Control.

[3]  Zhiqiang Gao,et al.  Active disturbance rejection control: a paradigm shift in feedback control system design , 2006, 2006 American Control Conference.

[4]  Yi Huang,et al.  An alternative paradigm for control system design , 2001 .

[5]  Hebertt Sira-Ramírez,et al.  Sliding Mode Control: The Delta-Sigma Modulation Approach , 2015 .

[6]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[7]  M. Hoagland,et al.  Feedback Systems An Introduction for Scientists and Engineers SECOND EDITION , 2015 .

[9]  Arindam Ghosh,et al.  Frequency-domain characterization of sliding mode control of an inverter used in DSTATCOM application , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[10]  Christopher Edwards,et al.  Sliding mode control : theory and applications , 1998 .

[11]  Carlos García-Rodriguez,et al.  On the Control of the Permanent Magnet Synchronous Motor: An Active Disturbance Rejection Control Approach , 2014, IEEE Transactions on Control Systems Technology.

[12]  Andrew R. Teel,et al.  ESAIM: Control, Optimisation and Calculus of Variations , 2022 .

[13]  Vadim I. Utkin,et al.  Sliding Modes and their Application in Variable Structure Systems , 1978 .

[14]  Congzhi Huang,et al.  Equivalence Among Flat Filters, Dirty Derivative-Based PID Controllers, ADRC, and Integral Reconstructor-Based Sliding Mode Control , 2020, IEEE Transactions on Control Systems Technology.